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André–Oort Conjecture
In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem (and is actually proven in several genuinely different ways). The conjecture concerns itself with a characterization of the Zariski closure of sets of special points in Shimura varieties. A special case of the conjecture was stated by Yves André in 1989 and a more general statement (albeit with a restriction on the type of the Shimura variety) was conjectured by Frans Oort in 1995. The modern version is a natural generalization of these two conjectures. Statement The conjecture in its modern form is as follows. Each irreducible component of the Zariski closure of a set of special points in a Shimura variety is a special subvariety. André's first version of the conjecture was just for one dimensional irreducible components, while Oort proposed that it should be true f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Umberto Zannier
Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) is an Italian mathematician, specializing in number theory and Diophantine geometry. Education Zannier earned a Laurea degree from University of Pisa and studied at the Scuola Normale Superiore di Pisa with Ph.D. supervised by Enrico Bombieri. Career Zannier was from 1983 to 1987 a researcher at the University of Padua, from 1987 to 1991 an associate professor at the University of Salerno, and from 1991 to 2003 a full professor at the Università IUAV di Venezia. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa. In 2010 he gave the Hermann Weyl Lectures at the Institute for Advanced Study. He was a visiting professor at several institutions, including the Institut Henri Poincaré in Paris, the ETH Zurich, and the Erwin Schrödinger Institute in Vienna. With Jonathan Pila he developed a method (now known as the Pila-Zannier method) of applying O-minimality to number-theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert F
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and '' berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hélène Esnault
Hélène Esnault (born 17 July 1953) is a French and German mathematician, specializing in algebraic geometry. Biography Born in Paris, Esnault earned her PhD in 1976 from the University of Paris VII. She wrote her dissertation on ''Singularites rationnelles et groupes algebriques'' (Rational singularities and algebraic groups) under the direction of Lê Dũng Tráng. She did her habilitation at the University of Bonn in 1985, and pursued her studies at the University of Duisburg-Essen. Afterwards, she was a Heisenberg scholar of the Deutsche Forschungsgemeinschaft (DFG) at the Max Planck Institute for Mathematics in Bonn. She became the first Einstein Professor at Freie Universität Berlin in 2012, as head of the algebra and number theory research group, after working previously at the University of Duisburg-Essen, the Max-Planck-Institut für Mathematik in Bonn, and at the University of Paris VII. In 2007 Esnault was editor-in-chief and founder of the journal Algebra & Num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shou-Wu Zhang
Shou-Wu Zhang (; born October 9, 1962) is a Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University. Biography Early life Shou-Wu Zhang was born in Hexian, Ma'anshan, Anhui, China on October 9, 1962. Zhang grew up in a poor farming household and could not attend school until eighth grade due to the Cultural Revolution. He spent most of his childhood raising ducks in the countryside and self-studying mathematics textbooks that he acquired from sent-down youth in trades for frogs. By the time he entered junior high school at the age of fourteen, he had self-learned calculus and had become interested in number theory after reading about Chen Jingrun's proof of Chen's theorem which made substantial progress on Goldbach's conjecture. Education Zhang was admitted to the Sun Yat-sen University chemistry department in 1980 after scoring poorly on his mathematics entrance examinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xinyi Yuan
Xinyi Yuan (; born 1981) is a Chinese mathematician who is currently a professor of mathematics at Peking University working in number theory, arithmetic geometry, and automorphic forms. In particular, his work focuses on arithmetic intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions. Education Yuan is from Macheng, Huanggang, Hubei province, and graduated from Huanggang Middle School in 2000. That year, he received a gold medal at the International Mathematical Olympiad while representing China. Yuan obtained his A.B. in mathematics from Peking University in 2003 and his Ph.D. in mathematics from the Columbia University in 2008 under the direction of Shou-Wu Zhang. His article "Big Line Bundles over Arithmetic Varieties," published in Inventiones Mathematicae, demonstrates a natural sufficient condition for when the Group action (mathematics)#Orbits and stabilizers, orbit under the absolute Galois group is equidistributed. Career He sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colmez Conjecture
Colmez is a French surname. It may refer to: * Pierre Colmez, French mathematician * Coralie Colmez Coralie Colmez is a French author and tutor in mathematics and mathematics education. Early life and career Coralie Colmez is the daughter of mathematicians Pierre Colmez and Leila Schneps. Colmez was raised in Paris, France. After completing ..., French mathematician and author (daughter of Pierre Colmez) {{Surname French-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Tsimerman
Jacob Tsimerman (born 1988) is a Canadian mathematician at the University of Toronto specialising in number theory and related areas. He was awarded the SASTRA Ramanujan Prize in the year 2015 in recognition for his work on the André–Oort conjecture and for his work in both analytic number theory and algebraic geometry. Education He studied at the University of Toronto, graduating in 2006 with a bachelor's degree in math. He obtained his PhD from Princeton in 2011 under the guidance of Peter Sarnak. Career Jacob Tsimerman was born in Kazan, Russia, on April 26, 1988. In 1990 his family first moved to Israel and then in 1996 to Canada. In 2003 and 2004 he represented Canada in the International Mathematical Olympiad (IMO) and won gold medals both years, with a perfect score in 2004. Following his PhD, he had a post-doctoral position at Harvard University as a Junior Fellow of the Harvard Society of Fellows. In July 2014 he was awarded a Sloan Fellowship and he started hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siegel Modular Form
In mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional ''elliptic'' modular forms which are closely related to elliptic curves. The complex manifolds constructed in the theory of Siegel modular forms are Siegel modular varieties, which are basic models for what a moduli space for abelian varieties (with some extra level structure) should be and are constructed as quotients of the Siegel upper half-space rather than the upper half-plane by discrete groups. Siegel modular forms are holomorphic functions on the set of symmetric ''n'' × ''n'' matrices with positive definite imaginary part; the forms must satisfy an automorphy condition. Siegel modular forms can be thought of as multivariable modular forms, i.e. as special functions of several complex variables. Siegel modular forms were first investigated by for the purpose of studying quadratic forms analytically. These primarily arise in various branches of number theory, su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clay Research Award
__NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class="wikitable sortable" , - ! Year !! Winner !! Citation , - , 2022 , , Søren Galatius and Oscar Randal-Williams John Pardon , , "for their profound contributions to the understanding of high dimensional manifolds and their diffeomorphism groups; they have transformed and reinvigorated the subject." "in recognition of his wide-ranging and transformative work in geometry and topology, particularly his groundbreaking achievements in symplectic topology." , - , 2021 , , Bhargav Bhatt , , "For his groundbreaking achievements in commutative algebra, arithmetic algebraic geometry, and topology in the p-adic setting." , - , 2020 , , not awarded , - , 2019 , , Wei Zhang Tristan Buckmaster, Philip Isett and Vlad Vicol , , "In recog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Curve
In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves ''X''(Γ) which are compactifications obtained by adding finitely many points (called the cusps of Γ) to this quotient (via an action on the extended complex upper-half plane). The points of a modular curve parametrize isomorphism classes of elliptic curves, together with some additional structure depending on the group Γ. This interpretation allows one to give a purely algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are defined either over the field of rational numbers Q or a cyclotomic field Q(ζ''n''). The latter fact and its generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
